Topological Properties of Real Normed Space

Pole DC	Wartość	Język
dc.contributor.author	Nakasho, Kazuhisa	-
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2015-12-09T20:41:02Z	-
dc.date.available	2015-12-09T20:41:02Z	-
dc.date.issued	2014	-
dc.identifier.citation	Formalized Mathematics, Volume 22, Issue 3, 2014, Pages 209-223	-
dc.identifier.issn	1426-2630	-
dc.identifier.issn	1898-9934	-
dc.identifier.uri	http://hdl.handle.net/11320/3720	-
dc.description.abstract	In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered here. Then we argue the condition when real normed subspaces become Banach’s spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67).	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	functional analysis	-
dc.subject	normed linear space	-
dc.subject	topological vector space	-
dc.title	Topological Properties of Real Normed Space	-
dc.type	Article	-
dc.identifier.doi	10.2478/forma-2014-0024	-
dc.description.Affiliation	Nakasho Kazuhisa - Shinshu University Nagano, Japan	-
dc.description.Affiliation	Futa Yuichi - Japan Advanced Institute of Science and Technology Ishikawa, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University Nagano, Japan	-
dc.description.references	Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.	-
dc.description.references	Nicolas Bourbaki, H.G. Eggleston, and S. Madan. Elements of mathematics: Topological vector spaces. Springer-Verlag, 1987.	-
dc.description.references	Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.	-
dc.description.references	Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.	-
dc.description.references	Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.	-
dc.description.references	Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.	-
dc.description.references	Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.	-
dc.description.references	Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama. Real linear space of real sequences. Formalized Mathematics, 11(3):249-253, 2003.	-
dc.description.references	Noboru Endou, Yasunari Shidama, and Katsumasa Okamura. Baire’s category theorem and some spaces generated from real normed space. Formalized Mathematics, 14(4): 213-219, 2006. doi:10.2478/v10037-006-0024-x.	-
dc.description.references	Adam Grabowski. On the boundary and derivative of a set. Formalized Mathematics, 13 (1):139-146, 2005.	-
dc.description.references	Jarosław Kotowicz. Convergent real sequences. Upper and lower bound of sets of real numbers. Formalized Mathematics, 1(3):477-481, 1990.	-
dc.description.references	Jarosław Kotowicz. Quotient vector spaces and functionals. Formalized Mathematics, 11 (1):59-68, 2003.	-
dc.description.references	Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.	-
dc.description.references	Keiko Narita, Noboru Endou, and Yasunari Shidama. Dual spaces and Hahn-Banach theorem. Formalized Mathematics, 22(1):69-77, 2014. doi:10.2478/forma-2014-0007.	-
dc.description.references	Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.	-
dc.description.references	Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.	-
dc.description.references	Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.	-
dc.description.references	Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.	-
dc.description.references	Walter Rudin. Functional Analysis. New York, McGraw-Hill, 2nd edition, 1991.	-
dc.description.references	Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.	-
dc.description.references	Yasunari Shidama. The series on Banach algebra. Formalized Mathematics, 12(2):131-138, 2004.	-
dc.description.references	Yasumasa Suzuki, Noboru Endou, and Yasunari Shidama. Banach space of absolute summable real sequences. Formalized Mathematics, 11(4):377-380, 2003.	-
dc.description.references	Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1): 115-122, 1990.	-
dc.description.references	Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.	-
dc.description.references	Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.	-
dc.description.references	Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Formalized Mathematics, 1(2):297-301, 1990.	-
dc.description.references	Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.	-
dc.description.references	Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990.	-
dc.description.references	Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865-870, 1990.	-
dc.description.references	Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.	-
dc.description.references	Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.	-
dc.description.references	Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.	-
dc.description.references	Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.	-
dc.description.references	Kosaku Yoshida. Functional Analysis. Springer, 1980.	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2014, Volume 22, Issue 3

Pliki w tej pozycji:

Plik	Opis	Rozmiar	Format
forma-2014-0024.pdf		295,02 kB	Adobe PDF	Otwórz

Pokaż uproszczony widok rekordu Zobacz statystyki

Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL